In the field of medicines and agricultural chemicals, one of the optical isomers of a compound shows especially excellent action in many cases. Particularly, a large number of optically active substances of carboxylic acids show excellent properties when each substance has an asymmetric carbon atom at the .alpha.- or .beta.-position.
With regard to the synthesis of these optically active carboxylic acids by asymmetric hydrogenation reaction, there are known processes in which a complex of an optically active phosphine compound with a transition metal is used as a catalyst of the asymmetric hydrogenation. Examples of such processes include a process which uses a complex of a phosphine having an optically active binaphthyl structure with ruthenium (JP-A-63-239245; the term "JP-A" as used herein means an "unexamined published Japanese patent application") and a process for the production of optically active phenylacetic acid derivatives using a complex of a transition metal with a phosphine having an optically active binaphthyl structure (JP-A-64-9952).
However, the prior art processes described above are defective in that the asymmetric yield of the reaction product is generally low although the product has a high optical purity, or that the optical purity of the reaction product is low although the asymmetric yield thereof is high. Namely, the above processes have failed to attain both a satisfactory optical purity and a satisfactory asymmetric yield. The prior art processes therefore are not industrially advantageous processes.